LONDON (Reuters) - Tesco <TSCO.L>, Britain's biggest grocery chain, has pulled dozens of Unilever <ULVR.L> <UNc.AS> brand products from its website after a disagreement over prices in the wake of a partly Brexit-driven slump in the British currency.

The dispute between two of Britain's best-known companies shows how the UK's decision to quit the European Union has exacerbated tensions between suppliers and retailers, which are battling for profits as consumers are increasingly savvy about their shopping.

Unilever has been trying to raise the prices it charges Britain's big four supermarkets - Tesco, Sainsbury's <SBRY.L>, Asda <WMT.N> and Morrisons <MRW.L> - across a wide range of goods by about 10 percent, saying it needs to offset the higher cost of imported commodities, two people with knowledge of the situation told Reuters.

One person with knowledge of the situation at a big four grocer said they had protested against Unilever's demands, noting that some of the products they wanted to charge more for are actually made in Britain.

"What’s really a problem is when a supplier like Unilever comes and asks for across the board cost increases and there's no negotiation, there's no discussion. That’s been the approach that's upset the grocers," he said, adding that no decision had been made whether to accept Unilever's demand or delist some products.

As of Wednesday evening, Unilever products - including Marmite spread, Ben & Jerry's ice cream, Lynx body spray and PG tips tea - were unavailable on Tesco's website, but the shortage had not yet affected stores, a Tesco spokesman said.

"We are currently experiencing availability issues on a number of Unilever products. We always work to ensure customers get the best possible prices and we hope to have this issue resolved soon," he said.

A spokesman for Unilever, which will report financial results on Thursday, declined to comment.

Last week, Tesco boss Dave Lewis, a former senior Unilever executive, hailed a transformed relationship with suppliers as a major factor in the grocer reporting a 60 percent rise in first-half profit and the setting of tougher profitability targets. But he indicated it was not a given that suppliers should be able to recoup the cost of the falling pound as they had not always passed on benefits when sterling was much stronger.

Since Britain's shock Brexit decision in June its currency has plunged almost 18 percent against the U.S. dollar.

Most analysts and economists believe that sterling's slump will lead to higher grocery prices, following years of deflation due to a price war between the big chains.

However, last month Mike Coupe, CEO of Sainsbury's <SBRY.L>, Britain's No. 2 supermarket, said the currency's depreciation would not necessarily lead to higher grocery prices, as it could be offset by lower commodities prices and stiff competition.

Three-quarters of British food manufacturers said they have seen an increase in the price of imported ingredients, according to a survey published earlier on Wednesday.

The average price for a basket of 35 commonly bought goods cost 83.19 pounds ($103.45) in September, according to price tracker, up 57 pence from May, the month before the referendum.

Sainsbury's and Morrisons declined to comment. Asda could not be immediately reached for comment.

(Reporting by Martinne Geller and James Davey in London; editing by Ralph Boulton, G Crosse)